What is degree of dissociation of CH ₃ COOH if ^ ( CH ₃ COO ⁻ )=50 ~S ~cm ^2 ~mol ⁻¹ , ^ ( H ⁺ )=350 ~S ~cm ^2 ~mol ⁻¹ and molar conductivity of 5 10⁻² M CH ₃ COOH is 20 ~S ~cm ^2 ~mol ⁻¹ ?

Step-by-step solution

The degree of dissociation for acetic acid is determined from the ratio of its molar conductivity at concentration c = 5 10⁻² , M to its limiting molar conductivity: = _m _m^ . Using Kohlrausch's law, the limiting molar conductivity is the sum of the limiting ionic conductivities: _m^ ( CH ₃ COOH ) = ^ ( CH ₃ COO ⁻) + ^ ( H ⁺) = 50 + 350 = 400 , S ,cm ^2 , mol ⁻¹ . Given _m = 20 , S ,cm ^2 , mol ⁻¹ , we find = 20 400 = 0.05 = 5 10⁻² . The value corresponds to option C .